Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity

@article{Colli2012,
abstract = {An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions. This system is meant to model two-species phase segregation on an atomic lattice under the presence of diffusion. A similar system has been recently introduced and analyzed in [3]. Both systems conform to the general theory developed in [5]: two parabolic PDEs, interpreted as balances of microforces and microenergy, are to be solved for the order parameter $\rho$ and the chemical potential $\mu$. In the system studied in this note, a phase-field equation in $\rho$ fairly more general than in [3] is coupled with a highly nonlinear diffusion equation for $\mu$, in which the diffusivity coefficient is allowed to depend nonlinearly on both variables.},
author = {Colli, Pierluigi, Gilardi, Gianni, Podio-Guidugli, Paolo, Sprekels, Jürgen},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {495-513},
publisher = {Unione Matematica Italiana},
title = {Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity},
url = {http://eudml.org/doc/290927},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Colli, Pierluigi
AU - Gilardi, Gianni
AU - Podio-Guidugli, Paolo
AU - Sprekels, Jürgen
TI - Global Existence for a Strongly Coupled Cahn-Hilliard System with Viscosity
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/10//
PB - Unione Matematica Italiana
VL - 5
IS - 3
SP - 495
EP - 513
AB - An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions. This system is meant to model two-species phase segregation on an atomic lattice under the presence of diffusion. A similar system has been recently introduced and analyzed in [3]. Both systems conform to the general theory developed in [5]: two parabolic PDEs, interpreted as balances of microforces and microenergy, are to be solved for the order parameter $\rho$ and the chemical potential $\mu$. In the system studied in this note, a phase-field equation in $\rho$ fairly more general than in [3] is coupled with a highly nonlinear diffusion equation for $\mu$, in which the diffusivity coefficient is allowed to depend nonlinearly on both variables.
LA - eng
UR - http://eudml.org/doc/290927
ER -